General Q&A for Class 12 · Page 197
5,215 free answers in General for Class 12 students, across CBSE, ICSE and State boards.
Question & Answer
Questions
- GeneralClass 12All
What is Snell's Law Full Formula?
The complete formula for Snell's Law is: n₁ sin θ₁ = n₂ sin θ₂ Where: n₁ = refractive index of the first medium θ₁ = angle of incidence (measured from the normal) n₂ = refractive index of the second medium θ₂ = angle of refraction (measured from the normal) Alternatively, it can be written as: sin θ₁ / sin θ₂ = n₂ / n₁ = v₁ / v₂, where v represents the velocity of light in each medium.
- GeneralClass 12All
Why is it Called Snell's Law?
The law is named after Willebrord Snellius, a Dutch astronomer and mathematician who formulated the mathematical relationship in 1621. Although the phenomenon of refraction was known to earlier scientists, Snellius was credited with providing the precise mathematical description we use today. The anglicized version of his name, "Snell," became attached to the law in English-speaking countries.
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What is Snell's Law in Vector Form?
In vector form, Snell's Law can be expressed as: n₁ (n̂ × î) = n₂ (n̂ × r̂) Where: n̂ = unit normal vector to the interface î = unit vector in the direction of incident ray r̂ = unit vector in the direction of refracted ray × represents the cross product This vector formulation is particularly useful in computer graphics and three-dimensional ray tracing applications.
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What Kind of Math is Snell's Law?
Snell's Law involves trigonometry, specifically the sine function and inverse sine (arcsin). It's typically taught in high school physics and reuires understanding of: Basic trigonometric ratios Angle measurement Algebraic manipulation Inverse functions Sometimes logarithms for advanced applications The math level is generally appropriate for students who have completed basic geometry and trigonometry.
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How to Solve Snell's Law Problems?
Here's a step-by-step approach: Draw a diagram showing the two media, normal line, incident ray, and refracted ray Label all known values (angles and refractive indices) Write down Snell's Law: n₁ sin θ₁ = n₂ sin θ₂ Substitute known values into the euation Solve algebraically for the unknown variable Use a calculator to find inverse sine if needed Check that your answer makes physical sense (e.g., light ben
- GeneralClass 12All
How to Use Snell's Law of Refraction?
To use Snell's Law, follow these steps: Identify the two media and find their refractive indices (n₁ and n₂) Measure or identify the angle of incidence (θ₁) from the normal Apply the formula: n₁ sin θ₁ = n₂ sin θ₂ Solve for the unknown angle: θ₂ = sin⁻¹[(n₁ sin θ₁) / n₂] Remember, angles are always measured from the normal (perpendicular line) to the surface, not from the surface itself.
- GeneralClass 12All
What is Refractive Index and How Does it Relate to Snell's Law?
The refractive index (n) is a measure of how much a material slows down light compared to its speed in a vacuum. It's calculated as n = c/v, where c is the speed of light in vacuum and v is the speed in the medium. The refractive index is central to Snell's Law because it determines how much light will bend at an interface. Materials with higher refractive indices (like glass or water) bend light more than materials with lower refractive indices (like air).
- GeneralClass 12All
What is the Basic Principle of Refraction?
The basic principle of refraction is that light changes speed when it moves from one transparent medium to another, causing it to change direction. This occurs because light travels at different velocities in different materials. When light enters a denser medium, it slows down and bends toward the normal; when it enters a less dense medium, it speeds up and bends away from the normal.
- GeneralClass 12All
What are the Three Laws of Refraction?
While traditionally there are two laws of refraction, some sources describe three aspects: The incident ray, refracted ray, and normal lie in the same plane Snell's Law: n₁ sin θ₁ = n₂ sin θ₂ The refracted ray lies on the opposite side of the normal from the incident ray These three statements together completely describe the behavior of light during refraction.
- GeneralClass 12All
What are the Two Laws of Refraction?
The two fundamental laws of refraction are: First Law: The incident ray, refracted ray, and normal to the surface at the point of incidence all lie in the same plane. Second Law (Snell's Law): The ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant for two given media, eual to the ratio of their refractive indices.
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What is Snell's Law Using Wave Theory?
Using wave theory, Snell's Law can be derived from the principle that the freuency of light remains constant as it passes between media, but its wavelength and speed change. Since the wavefronts must remain continuous at the boundary, the relationship becomes: λ₁ / λ₂ = v₁ / v₂ = sin θ₁ / sin θ₂, where λ represents wavelength and v represents velocity. This connects to the refractive index formula, as n = c/v (speed of light in vacuum divided by speed in mediu
- GeneralClass 12All
7. What is the Real Name of Snell's Law?
Snell's Law is also known as the "Law of Refraction" or "Snell-Descartes Law." It's named after Dutch mathematician Willebrord Snellius (1580-1626), who described it in 1621, though the principle was also independently discovered by French philosopher René Descartes. In some scientific literature, it's simply referred to as the "law of sines" in refraction.
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6. Why is Snell's Law Important?
Snell's Law is crucial because it explains and predicts how light behaves when moving between different materials. This principle is essential for designing optical instruments like eyeglasses, cameras, microscopes, and telescopes. It also helps us understand natural phenomena like rainbows, mirages, and why objects appear bent when partially submerged in water. Without Snell's Law, modern optics and many medical technologies wouldn't exist.
- GeneralClass 12All
5. What is the Second Law of Refraction (Snell's Law)?
The second law of refraction, commonly called Snell's Law, states that the ratio of the sine of the angle of incidence to the sine of the angle of refraction is constant for a given pair of media. This constant is eual to the ratio of the refractive indices of the two media. This is the mathematical relationship: n₁ sin θ₁ = n₂ sin θ₂.
- GeneralClass 12All
4. What is Snell's First Law?
Snell's First Law, also known as the first law of refraction, states that the incident ray, the refracted ray, and the normal to the interface at the point of incidence all lie in the same plane. This means all three lines are flat on one surface together, not scattered in three-dimensional space.
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3. What is Snell's Law for Class 10 (Easy Explanation)?
For Class 10 students, Snell's Law can be understood simply: when light travels from one material to another (like from air to water), it changes direction. The amount it bends depends on how different the two materials are. The formula n₁ sin θ₁ = n₂ sin θ₂ helps us calculate exactly how much the light will bend. Think of it like a car moving from pavement onto sand it slows down and changes direction.
- GeneralClass 12All
What is Kepler's third law T²/r³?
Kepler's Third Law states that the suare of a planet's orbital period (T²) is proportional to the cube of its average distance from the Sun (r³). Mathematically: T²/r³ = constant for all planets orbiting the same star. More precisely, T² = (4π²/GM)r³, where G is the gravitational constant and M is the Sun's mass. This law reveals the fundamental relationship between orbital distance and period.
- GeneralClass 12All
How to use the formula = mcΔT?
To use = mcΔT, identify the mass (m) in grams or kilograms, specific heat capacity (c) in J/(g·°C) or J/(kg·°C), and temperature change (ΔT = T_final - T_initial). Multiply these three values to find the heat energy () transferred. For example, heating 100g of water by 10°C reuires = 100 × 4.18 × 10 = 4,180 joules.
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What is √(GM/r)?
The expression √(GM/r) represents orbital velocity, the speed reuired for an object to maintain a circular orbit around a massive body. G is the gravitational constant, M is the mass of the central body (like Earth), and r is the orbital radius from the center. This formula shows that orbital velocity decreases with distance—satellites farther from Earth move slower.
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What is U = -GMm/R?
The euation U = -GMm/R represents gravitational potential energy between two masses. G is the universal gravitational constant, M and m are the two masses, and R is the distance between their centers. The negative sign indicates that gravitational potential energy is zero at infinite separation and becomes more negative as objects approach each other, reflecting the attractive nature of gravity.